This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...) and the ontological commitments underlying the stylistic practice. (shrink)

The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied by many interpreters in seeking for specific logical rules at work in ancient mathematical texts.

Objective: To investigate the differences between patients returning to work and those who did not after brain tumor surgery.Methods: Patients were evaluated before surgery and after 3 months. The Montreal Cognitive Assessment test, Trail-Making Test, 15-word Rey–Osterrieth Word List, F-A-S tests, and Karnosfky Performance Status were used to assess cognitive status, attention, executive functions, memory, word fluency, and functional status. Patient-reported outcome measures used to evaluate emotional distress and disability were the Hospital Anxiety and Depression Scale and World Health Organization (...) Disability Assessment Schedule. Clinical and work-related variables, PROMs, and cognitive tests were compared using chi-squared, t-test or Mann–Whitney U test.Results: Sixty patients were included. Patients returning to work were 61.3 and 31.0% among people with meningioma and glioma, respectively. They reported lower postoperative disability and lesser home-to-work travel time. Patients with meningioma also showed better preoperative and postoperative attention and executive functions, better postoperative functional and cognitive status, and lower frequency of treatments.Conclusions: These variables should be considered in a clinical context to plan interventions for people who need support during return to work and in future research to investigate preoperative and postoperative predictive factors of going back to work. (shrink)

This landmark work provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics, from the "new theory of reference" and non-linguistic necessity and essentialism to "Kripke semantics.".

Cultural evolution studies are characterized by the notion that culture evolves accordingly to broadly Darwinian principles. Yet how far the analogy between cultural and genetic evolution should be pushed is open to debate. Here, we examine a recent disagreement that concerns the extent to which cultural transmission should be considered a preservative mechanism allowing selection among different variants, or a transformative process in which individuals recreate variants each time they are transmitted. The latter is associated with the notion of “cultural (...) attraction”. This issue has generated much misunderstanding and confusion. We first clarify the respective positions, noting that there is in fact no substantive incompatibility between cultural attraction and standard cultural evolution approaches, beyond a difference in focus. Whether cultural transmission should be considered a preservative or reconstructive process is ultimately an empirical question, and we examine how both preservative and reconstructive cultural transmission has been studied in recent experimental research in cultural evolution. Finally, we discuss how the relative importance of preservative and reconstructive processes may depend on the granularity of analysis and the domain being studied. (shrink)

ABSTRACTThe presence of emotional words and content in stories has been shown to enhance a story’s memorability, and its cultural success. Yet, recent cultural trends run in the opposite direction. Using the Google Books corpus, coupled with two metadata-rich corpora of Anglophone fiction books, we show a decrease in emotionality in English-speaking literature starting plausibly in the nineteenth century. We show that this decrease cannot be explained by changes unrelated to emotionality, and that, in our three corpora, the decrease is (...) driven almost entirely by a decline in the proportion of positive emotion-related words, while the frequency of negative emotion-related words shows little if any decline. Consistently with previous studies, we also find a link between ageing and negative emotionality at the individual level. (shrink)

Cultural evolution researchers use transmission chain experiments to investigate which content is more likely to survive when transmitted from one individual to another. These experiments resemble oral storytelling, wherein individuals need to understand, memorize, and reproduce the content. However, prominent contemporary forms of cultural transmission—think an online sharing—only involve the willingness to transmit the content. Here I present two fully preregistered online experiments that explicitly investigated the differences between these two modalities of transmission. The first experiment (_N_ = 1,080 participants) (...) examined whether negative content, information eliciting disgust, and threat-related information were better transmitted than their neutral counterpart in a traditional transmission chain setup. The second experiment (_N_ = 1,200 participants) used the same material, but participants were asked whether or not they would share the content in two conditions: in a large anonymous social network or with their friends, in their favorite social network. Negative content was both better transmitted in transmission chain experiments and shared more than its neutral counterpart. Threat-related information was successful in transmission chain experiments but not when sharing, and finally, information eliciting disgust was not advantaged in either. Overall, the results present a composite picture, suggesting that the interactions between the specific content and the medium of transmission are important and, possibly, that content biases are stronger when memorization and reproduction are involved in the transmission—as in oral transmission—than when they are not—as in online sharing. Negative content seems to be reliably favored in both modalities of transmission. (shrink)

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, (...) a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context. (shrink)

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

ArgumentThis article is the sequel to an article published in the previous issue ofScience in Contextthat dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show thatthere wasa well-establishedmathematicalfield of discourse in “foundations (...) of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations. (shrink)

Book 1 of Euclid's Elements opens with a set of unproved assumptions: definitions, postulates, and ‘common notions’. The common notions are general rules validating deductions that involve the relations of equality and congruence. The attested postulates are five in number, even if a part of the manuscript tradition adds a sixth, almost surely spurious, that in some manuscripts features as the ninth, and last, common notion. The postulates are called αἰτήματα both in the manuscripts of the Elements and in the (...) ancient exegetic tradition. It is not said, however, that this denomination is original, as it coincides with the nomen rei actae associated with the verbal form introducing the postulates themselves. Since antiquity it has been recognized that the postulates naturally split into two groups of quite different character: the first three are rules licensing basic constructions, the fourth and the fifth are assertions stating properties of particular geometric objects. I transcribe postulates 1–3 in the text established by Heiberg : ᾐτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖνκαὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖνκαὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράϕεσθαι. (shrink)

We experimentally investigated the influence of context-based biases, such as prestige and popularity, on the preferences for quotations. Participants were presented with random quotes associated to famous or unknown authors, or with random quotes presented as popular, i.e. chosen by many previous participants, or unpopular. To exclude effects related to the content of the quotations, all participants were subsequently presented with the same quotations, again associated to famous and unknown authors, or presented as popular or unpopular. Overall, our results showed (...) that context-based biases had no, or limited, effect in determining participants’ choices. Quotations preferred for their content were preferred in general, despite the contextual cues to which they were associated. We conclude discussing how our results fit with the well-known phenomenon of the spread and success of misattributed quotations, and we draw some more general implications for cultural evolution research. (shrink)

The aim of this article is to present and discuss the language of the «givens», a typical stylistic resource of Greek mathematics and one of the major features of the proof format of analysis and synthesis. I shall analyze its expressive function and its peculiarities, as well as its general role as a deductive tool, explaining at the same time its particular applications in subgenres of a geometrical proposition like the locus theorems and the so-called «porisms». The main interpretative theses (...) of this study are the following: the language of the «givens» (1) is the standard idiom in which “existence and uniqueness” of a mathematical object was proved, (2) was conceived as an unified framework reducing to a strictly deductive format disparate argumentative steps such as deductions, constructions, and calculations. (shrink)

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into St. (...) Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

The identification of a “new” handwriting of Manuel Chrysoloras allows to assign to him a number of hitherto unpublished witnesses, all preceding his teaching activity in Florence from 1397. This new dossier illustrates Chrysoloras’ youth in Constantinople, providing precious and so far unknown information on his family, his father John, his studies in the anti-Palamite milieux with Isaac Argyros and Demetrios Kydones, and, of course, his books, his graphic education, and his readings. Among these, a special place is occupied by (...) Aristotle’s logic: particular attention is therefore paid to a mock-up of a manuscript containing Aristotle’s Organon with a marginal commentary, here attributed to Chrysoloras and realized in a well-known manuscript by his master Argyros. (shrink)

General remarks about Cornelio Fabro's works on philosophical anthropology.

Folk-economic beliefs may be regarded as “evidential fictions” that exploit the natural tendency of human cognition to organize itself in narrative form. Narrative counter-arguments are likely more effective than logical debunking. The challenge is to convey sound economic reasoning in narratively conspicuous forms – an opportunity for economics to rethink its role and agency in public discourse, in the spirit of its old classics.

The article analyzes in detail the assumptions and the proofs typical of the research field of the geometry of burning mirrors. It emphasizes the role of two propositions of the Archimedean Quadratura parabolae, never brought to bear on this subject, and of a complex system of projections reducing a sumptōma of a parabola to some specific linear lemmas. On the grounds of this case-study, the much-debated problem of the heuristic role of analysis is also discussed.

The question of the trait that would distinguish human beings from the rest of the animals has kept humanity awake for centuries. Their ability to express themselves through words, their use of reason, their self-awareness of their finiteness or their capacity to produce and appreciate the art have been some of the faculties that, over the centuries, have come to give humanity a justification for its position in the world. With the advent of Artificial Intelligence, many of these attributes came (...) to be questioned thanks to the ability of non-biological entities to produce, among other performances, artistic and literary works. In this article we will revisit some of the topics that have allowed us to delineate the limits of what is human and, in the light of the latest technological advances, to question the link that humanity, technology and artistic creation have with each other today. (shrink)

En el presente artículo se analizan las transformaciones que, a partir del siglo IV, experimentan los obispos cristianos por su estrecha vinculación con el poder imperial: si en un principio Constantino quiso ponerlos a su servicio como estrechos colaboradores en la administración del Imperio, pronto algunos de ellos, con gran personalidad, se sirvieron de los honores y privilegios adquiridos para reclamar una independencia allí donde — a diferencia de lo que sucederá en Constantinopla a partir de Teodosio I— su elección (...) no dependía del emperador. (shrink)

Three problems in book I of Diophantus’ Arithmetica contain the adjective plasmatikon, that appears to qualify an implicit reference to some theorems in Elements, book II. The translation and meaning of the adjective sparked a long-lasting controversy that has become a nonnegligible aspect of the debate about the possibility of interpreting Diophantus’ approach and, more generally, Greek mathematics in algebraic terms. The correct interpretation of the word, a technical term in the Greek rhetorical tradition that perfectly fits the context in (...) which it is inserted in the Arithmetica, entails that Diophantus’ text contained no (implicit) reference to Euclid’s Elements. The clause containing the adjective turns out to be a later interpolation, that cannot be used to support any algebraic interpretation of the Arithmetica. (shrink)

General remarks on some ontological premises of Aquinas' Epistemology.

An analysis of personal self-determination with a special reference to Aquinas.

Philosophical reflections about the complex relationship between Jacobi and Fichte on realism and idealism.

An introduction to the first edition of a brief text written by Cornelio Fabro on Freedom.

The passage has been an object of scholarly debate: the lack of independent sources on the mathematical construction described by Aristotle, the terseness of the formulation and the resulting syntactical ambiguities make the exact interpretation of the text quite difficult, as already noted by Philoponus. What does it mean that the gnomons are ‘placed round the one and without’ (περὶ τὸ ἓν καὶ χωρίς)? And in what sense is this an indication of the even being ‘cut off, enclosed (ἐναπολαμβανόμενον), and (...) limited (περαινόμενον) by the odd’? The aim of the present paper is to discuss the available interpretations of the passage and to propose a new one. (shrink)

"Vocablo infaltable en todas las corrientes políticas occidentales, el republicanismo ha tendido a convertirse, en los últimos tiempos, es una suerte de significante vacío al que se apela sin más como sinónimo de justicia, de balance de poderes o de plena institucionalidad. En un libro que recupera el fundamental legado de Cicerón, Juan Acerbi presenta una serie de aspectos que se sumergen en las oscuras aguas de la tradición republicana para aclarar conceptos y aristas que, aún desde su latencia, (...) determinan muy de cerca el derrotero de las prácticas gubernamentales contemporáneas. Signado por el análisis de la performatividad del discurso político, de los usos de las justificaciones religiosas y de la íntima ligazón entre símbolos, formas de participación ciudadana, temporalidades y otros recursos para la conservación y ampliación del poder, este volumen recorre los meandros de la metapolítica para dejar al desnudo el cuerpo vivo del yo que sostiene a la república. Allí, el estudio sobre virtud del líder político, comprendido como un ser diferente del resto, demuestra que hace falta todavía sospechar de los vínculos entre un republicanismo cargado de razón pública y el capitalismo, que pretende que determinadas formas vacuas, exánimes, ocupen el lugar de los pensantes. A contrapelo de la desquiciada celebración de la inmediatez que se observa en nuestros días, Acerbi retoma un aspecto cardinal para cualquier pensamiento que pretenda ser político: la distinción entre lo necesario y lo contingente y la ubicación de toda acción política en el segundo de esos polos. De ese modo, apela a la palabra como forma fundamental de lo humano y logra ver, bajo un mismo cristal, eventos pasados, presentes y futuros que desenmascaran cualquier ilusión de una vida autoevidente." Hernán Borisonik. (shrink)

An interpretation of Jacobi's philosophical realism.